feat: modernize build tooling and add CI/CD workflow

Switch to Bun for 2-5x faster frontend builds, implement cargo-chef for
reliable Rust dependency caching, and add Biome for fast code
formatting.

Build system improvements:
- Replace pnpm with Bun for frontend package management
- Add cargo-chef to Dockerfile for better Rust build layer caching
- Update all commands to use bun instead of pnpm

Developer experience:
- Add comprehensive Justfile commands (format, format-check, db)
- Implement automated PostgreSQL Docker setup with random port
allocation
- Add stricter checks (--deny warnings on clippy, --all-features flag)

Code quality:
- Add Biome formatter for 10-100x faster TypeScript/JavaScript
formatting
- Add GitHub Actions CI/CD workflow for automated checks
- Update .dockerignore with comprehensive exclusions
- Format all code with cargo fmt (Rust) and Biome (TypeScript)

All changes maintain backward compatibility and can be tested
incrementally.

README.md

@@ -26,7 +26,7 @@ The application consists of three modular services that can be run independently
 ## Quick Start
 
 ```bash
-pnpm install -C web  # Install frontend dependencies
+bun install --cwd web  # Install frontend dependencies
 cargo build  # Build the backend
 
 just dev # Runs auto-reloading dev build